2023 ieee 16th international conference of actual problems of electronic instrument engineering (apeie)

II.Mathematical Study of Electrical Systems

Electrical system the electrical part of the energy system, that is, the set of elements that produce, transform, transmit, distribute and consume electrical energy.
The mathematical description of the electrical power system must necessarily have specific characteristics that differ from the thermal power or hydropower part of the system.
When creating a mathematical description, it is necessary to take into account the entry of power elements into the electrical system - generators, transformers, converters, loads and electrical networks (high voltage, medium voltage, relatively low voltage distribution, including power lines).
An electrical system also includes controls that change and regulate the state of the system or the mode of operation of the system. Mathematical hardware is needed to calculate the system mode. An engineer can take it ready-made from the vast arsenal of mathematical methods accumulated over the centuries, or partially design it himself. But this is possible if he accurately imagines the physics of the energy system, due to physical phenomena that occur simultaneously in all elements of the system. By interacting with each other, the elements of the system are connected at any time by the unity of the processes of production, transmission, distribution and consumption of electricity. At the same time,
Electrical and related mechanical processes must be taken into account when studying electrical energy generation, transmission, distribution, and control systems. For example, processes in prime movers (turbines) in which mechanical energy is converted into electrical energy in generators, and processes in electric motors in which electrical energy is converted into mechanical energy, which cannot be separated from the processes in the electrical part, are considered.
We should consider the processes occurring in the system as a single electromechanical. It is also important to remember that the elements that make up a system can reveal new properties and processes that occur in the system that combines these elements.
To give a mathematical description of the system, it is necessary to describe all the relationships between the process variables in the form of a mathematical model. The study of these processes, including their mathematical interpretation, is aimed at ensuring the best functioning of the system, the main task of which is the production of energy.

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  Energyis a quantitative indicator of the operation of the electrical system.
  
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  Qualityenergy is mainly characterized by the magnitude and frequency of the voltage in the consumer.
  

The model can also be used as a reference by solar cell manufacturers and in the experimental studies.